Our (small) company is a little late to the party on this, and we've only just realised that we're better off with an SSL certificate for our website. (Yes I know, I know, but we dropped SEO some time ago after getting severely bitten by a certain Penguin, and are only just making tentative step back to it after those intervening years, so we're running to get back up to date with these things.)
This has now been implemented, but our web guy has dropped the 'www' element during the process.
Our http://domain.com address has always historically been redicrected to our main http://www.domain.com address.
Now our web guy has implemented the SSL cert, our website URL is appearing as https://domain.com, and he has redirected the http://www.domain.com to that new URL.
Obviously all our historic (and more recent) link building has been to the http://www.domain.com address.
Is this an issue, should the new Https URL keep the 'www', or does it make no difference what so ever?
Conversely could it actually be of benefit dropping the 'www.' because our keyword specific product URL's are now 4 characters closer to the http and 4 digits shorter?
Finally, on the links we have control of (professional trade associations etc) do we need to ask them to change the links to the new Https address, or does the transition from Http to Https make no difference?